Calculus II
General
Prefix
MATH
Course Number
222
Course Level
Undergraduate
Department/Unit(s)
College/School
College of Science and Engineering
Description
Integration techniques and applications, inverse functions, topics in analytic geometry, sequences and series, improper integrals, plane curves.
Prerequisites
Credits
Min
4
Max
4
Repeatable
No
Goals and Diversity
MN Goal Course
Yes
MN Goal Designation(s)
04
Cultural Diversity
No
Learning Outcomes
Outcome
Use integration to find volumes of solids described via cross-section and solids of revolution, to find the lengths of curves, to find the surface area of a surface of revolution and to solve physical problems involving concepts such as work, hydrostatic force, and center of mass.
Outcome
Calculate integrals exactly by integration by parts, inspection of powers of trigonometric functions, trigonometric substitution, and partial fractions.
Outcome
Approximate integrals by using the Trapezoidal Rule, Simpson¿s Rule, and Taylor series.
Outcome
Use analytic methods to evaluate integrals whose integrands have asymptotes or whose interval of integration is infinite.
Outcome
Sketch curves given by parametric equations or polar equations, and represent given curves as parametric equations or polar equations.
Outcome
Convert points and equations from polar coordinates to Cartesian coordinates, and vice versa.
Outcome
Calculate areas, tangents, and lengths related to curves given by parametric or polar equations.
Outcome
Calculate limits of sequences by algebraic and numerical methods and the Squeeze Theorem.
Outcome
Identify geometric series, telescoping series, and the harmonic series and test series for convergence by using the integral test, the comparison tests, methods for working with alternating series, the ratio test, and the root test.
Outcome
Represent a given function as a power series over a suitable interval and find the interval of convergence of a given power series.
Outcome
Give the formulas and intervals of convergence for selected Taylor series such as the ones for the sine, cosine, inverse tangent, and natural exponential functions.
Outcome
State and apply named theorems of calculus (Bounded Monotonic Sequence Theorem, Taylor¿s Theorem).
Outcome
Communicate their knowledge of the principles of Calculus II, both orally (e.g. class discussions) and in writing (e.g. written assessments).
Dependencies
Courses
MATH222
is a
prerequisite
for:
Programs
MATH222
is a
completion requirement
for: